Problem: Solve for $z$, $- \dfrac{z + 1}{2z + 7} = \dfrac{1}{8} $
Answer: Multiply both sides of the equation by $2z + 7$ $ -(z + 1) = \dfrac{2z + 7}{8} $ Multiply both sides of the equation by $8$ $ -8(z + 1) = 2z + 7 $ $-8z - 8 = 2z + 7$ $-8 = 10z + 7$ $-15 = 10z$ $10z = -15$ $z = -\dfrac{15}{10}$ Simplify. $z = -\dfrac{3}{2}$